Optimal sequential measurements for bipartite state discrimination

State discrimination is a useful test problem with which to clarify the power and limitations of different classes of measurement. We consider the problem of discriminating between given states of a bipartite quantum system via sequential measurement of the subsystems, with classical feed-forward of measurement results. Our aim is to understand when sequential measurements, which are relatively easy to implement experimentally, perform as well, or almost as well, as optimal joint measurements, which are in general more technologically challenging. We construct conditions that the optimal sequential measurement must satisfy, analogous to the well-known Helstrom conditions for minimum error discrimination in the unrestricted case. We give several examples and compare the optimal probability of correctly identifying the state via global versus sequential measurement strategies

Optimal discrimination of single-qubit mixed states

We consider the problem of minimum-error quantum state discrimination for single-qubit mixed states. We present a method which uses the Helstrom conditions constructively and analytically; this algebraic approach is complementary to existing geometric methods, and solves the problem for any number of arbitrary signal states with arbitrary prior probabilities.Comment: 8 pages, 1 figur

Optimal discrimination of quantum states

Quantum state discrimination is a fundamental task in the field of quantum communication and quantum information theory. Unless the states to be discriminated are mutually orthogonal, there will be some error in any attempt to determine which state was sent. Several strategies to optimally discriminate between quantum states exist, each maximising some figure of merit. In this thesis we mainly investigate the minimum-error strategy, in which the probability of correctly guessing the signal state is maximised. We introduce a method for constructing the optimal Positive-Operator Valued Measure (POVM) for this figure of merit, which is applicable for arbitrary states and arbitrary prior probabilities. We then use this method to solve minimum-error state discrimination for the so-called trine states with arbitrary prior probabilities - the first such general solution for a set of quantum states since the two-state case was solved when the problem of state discrimination was first introduced. We also investigate the difference between local and global measurements for a bipartite ensemble of states, and find that in certain circumstances the local measurement is superior. We conclude by finding a bipartite analogue to the Helstrom conditions, which indicate when a POVM satisfies the minimum-error criteria

Optimal measurement strategies for the trine states with arbitrary prior probabilities

We investigate the optimal measurement strategy for state discrimination of the trine ensemble of qubit states prepared with arbitrary prior probabilities. Our approach generates the minimum achievable probability of error and also the maximum confidence strategy. Although various cases with symmetry have been considered and solution techniques put forward in the literature, to our knowledge this is only the second such closed form, analytical, arbitrary prior, example available for the minimum-error figure of merit, after the simplest and well-known two-state example

Optimal measurement strategies for the trine states with arbitrary prior probabilities

We investigate the optimal measurement strategy for state discrimination of the trine ensemble of qubit states prepared with arbitrary prior probabilities. Our approach generates the minimum achievable probability of error and also the maximum confidence strategy. Although various cases with symmetry have been considered and solution techniques put forward in the literature, to our knowledge this is only the second such closed form, analytical, arbitrary prior, example available for the minimum-error figure of merit, after the simplest and well-known two-state example

Assessment of proximal pulmonary arterial stiffness using magnetic resonance imaging:effects of technique, age and exercise

INTRODUCTION: To compare the reproducibility of pulmonary pulse wave velocity (PWV) techniques, and the effects of age and exercise on these. METHODS: 10 young healthy volunteers (YHV) and 20 older healthy volunteers (OHV) with no cardiac or lung condition were recruited. High temporal resolution phase contrast sequences were performed through the main pulmonary arteries (MPAs), right pulmonary arteries (RPAs) and left pulmonary arteries (LPAs), while high spatial resolution sequences were obtained through the MPA. YHV underwent 2 MRIs 6 months apart with the sequences repeated during exercise. OHV underwent an MRI scan with on-table repetition. PWV was calculated using the transit time (TT) and flow area techniques (QA). 3 methods for calculating QA PWV were compared. RESULTS: PWV did not differ between the two age groups (YHV 2.4±0.3/ms, OHV 2.9±0.2/ms, p=0.1). Using a high temporal resolution sequence through the RPA using the QA accounting for wave reflections yielded consistently better within-scan, interscan, intraobserver and interobserver reproducibility. Exercise did not result in a change in either TT PWV (mean (95% CI) of the differences: −0.42 (−1.2 to 0.4), p=0.24) or QA PWV (mean (95% CI) of the differences: 0.10 (−0.5 to 0.9), p=0.49) despite a significant rise in heart rate (65±2 to 87±3, p<0.0001), blood pressure (113/68 to 130/84, p<0.0001) and cardiac output (5.4±0.4 to 6.7±0.6 L/min, p=0.004). CONCLUSIONS: QA PWV performed through the RPA using a high temporal resolution sequence accounting for wave reflections yields the most reproducible measurements of pulmonary PWV

Allopurinol in Patients with Pulmonary Hypertension Associated with Chronic Lung Disease.

BACKGROUND: Oxidative stress (OS) has been implicated in the development of pulmonary hypertension (PH) and ventricular hypertrophy. Xanthine oxidase is a well-recognised source of reactive oxygen species, which lead to OS. The aim of this proof of concept study was to assess whether allopurinol (xanthine oxidase inhibitor) would reduce right ventricular mass (RVM) in patients with PH-associated chronic lung disease (PH-CLD). METHODS: We conducted a randomised, double-blind, parallel-group, placebo-controlled trial in patients with PH-CLD (93% COPD, 7% IPF) who were randomly assigned to receive allopurinol or placebo for 12 months. The primary outcome was the mean change in RVM, as assessed by cardiac magnetic resonance imaging (CMRI). Secondary outcomes included quality of life (QOL), spirometry and six-minute walk test (6MWT). RESULTS: Seventy-one patients were recruited: mean age 71 years, mean pulmonary arterial pressure 30 mm Hg, FEV1 60% and resting SpO2 96%. After 12 months, there was no significant difference in the change in RVM from baseline (allopurinol 1.85g vs placebo 0.97g with mean difference 0.88g, CI -4.77 to 3.01, p =0.7). There were also no significant changes in other cardiac parameters measured on MRI, in QOL, spirometry and 6MWT. Subgroup analysis showed that allopurinol significantly reduced RVM compared to placebo with -6.16g vs 0.75g and mean difference 6.92g (CI 1.14 to 12.69, p = 0.02) in COPD patients with more severe airflow limitation. CONCLUSION: Allopurinol had no overall impact on patients with PH-CLD but had potential benefit in COPD patients with more severe airflow limitation

Efficacy of noninvasive cardiac imaging tests in diagnosis and management of stable coronary artery disease

Ify R Mordi,1,2 Athar A Badar,2 R John Irving,2 Jonathan R Weir-McCall,1 J Graeme Houston,1 Chim C Lang1,2 1Division of Molecular and Clinical Medicine, University of Dundee, Dundee, UK; 2Department of Cardiology, Ninewells Hospital and Medical School, Dundee, UK Abstract: The aim of this review was to discuss the current literature regarding the utility of noninvasive imaging in diagnosis and management of stable coronary artery disease (CAD) including recent data from large randomized trials assessing diagnosis and prognosis. Current guidelines recommend revascularization in patients with refractory angina and in those with potential prognostic benefit. Appropriate risk stratification through noninvasive assessment is important in ensuring patients are not exposed to unnecessary invasive coronary angiograms. The past 20&nbsp;years have seen an unprecedented expansion in noninvasive imaging modalities for the assessment of stable CAD, with cardiovascular magnetic resonance and computed tomography complementing established techniques such as myocardial perfusion imaging, echocardiography and exercise electrocardiogram. In this review, we examine the current state-of-the-art in noninvasive imaging to provide an up-to-date analysis of current investigation and management options. Keywords: angina, noninvasive imaging, SPECT, stress echo, cardiovascular magnetic resonance, CT coronary angiograph

Comparing flow cytometry with culture-based methods for microbial monitoring and as a diagnostic tool for assessing drinking water treatment processes

Flow cytometry (FCM) and the ability to measure both total and intact cell populations through DNA staining methodologies has rapidly gained attention and consideration across the water sector in the past decade. In this study, water quality monitoring was undertaken over three years across 213 drinking water treatment works (WTW) in the Scottish Water region (Total n = 39,340). Samples subject to routine regulatory microbial analysis using culture-based methods were also analysed using FCM. In addition to final treated water, the bacterial content in raw water was measured over a one-year period. Three WTW were studied in further detail using on-site inter-stage sampling and analysis with FCM. It was demonstrated that there was no clear link between FCM data and the coliform samples taken for regulatory monitoring. The disinfectant Ct value (Ct = mg·min/L) was the driving factor in determining final water cell viability and the proportion of intact cells (intact/total cells) and the frequency of coliform detections in the water leaving the WTW. However, the free chlorine residual, without consideration of treatment time, was shown to have little impact on coliform detections or cell counts. Amongst the three treatment trains monitored in detail, the membrane filtration WTW showed the greatest log removal and robustness in terms of final water intact cell counts. Flow cytometry was shown to provide insights into the bacteriological quality of water that adds significant value over and above that provided by traditional bacterial monitoring